Theorems · Theorem · general topology
PiNat.firstDiff_comm
∀ {E : ℕ → Type u_1} (x y : (n : ℕ) → E n), PiNat.firstDiff x y = PiNat.firstDiff y x- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.findproof · cited by 139
- PiNat.firstDiffstatement · cited by 23
- Nat.find.congr_simpproof · cited by 11
- PiNat.firstDiff_defproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- PiNat.dist_commproof · cited by 2
- PiNat.exists_lipschitz_retraction_of_isClosedproof · cited by 2
- PiNat.cylinder_longestPrefix_eq_of_longestPrefix_lt_firstDiffproof · cited by 1
- PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinderproof · cited by 0